Extreme motion blur for particle bullet tracers
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This can happen with particles in fast motion. The issue is that they are basically moving too far within the time span of a frame for the calculation to happen correctly. The solution is to add subframes.

 

Try to increase this value by one or two. That usually solves it for me. Try more if needed.

Edit after testing the blend file:

Thanks for the blend file. I am seeing the same on the most recent build of 2.8. But I also I tested two things:


Particle movement without Camera-Shake.
NO particle movement but WITH camera shake.


(1) Looks fine, but (2) produces the weird behavior, even without particle movement. This seems like a bug to me, that you probably should report via "Help"-Menu > "Report a bug". (Update your Blender before doing so, because new builds come out every night. - So yours is already WAY out of date.)
This seems related, but you are with having the problem with different parameters.

In the meantime here's a possible workaround for your current scene, provided you have access to software with a "force motion blur" effect.

Render with the following changes:
 1. No camera shake.
 2. A wider image (decrease focal length)
 3. Increase the Output Resolution

You can place the result in a Composition with the actual dimensions of your final shot. Move the frame within the composition to fake the camera shake. (Which is essentially the same, since the camera in your blend file only rotates). Apply the "force motion blur" effect.

I know this is not perfect, but merely an idea to get you to the result you want.

Hope this helps.